netplot In a nutshell

• What: An R package for network visualization inspired by Gephi.

• Why: Opinionated way to visualize graphs.¹

• Where: You can get the dev version on GitHub (USCCANA/netplot) or the stable version on CRAN.

Main features

• Visualization engine: The grid system (same used by ggplot2.)

• Layout algorithms: Default uses igraph’s layout.

• Vertex sizes: Relative to the drawing area.

Example code+output

The personal friendship network of a faculty of a UK university, consisting of 81 vertices (individuals) and 817 directed and weighted connections. The school affiliation of each individual is stored as a vertex attribute. This dataset can serve as a testbed for community detection algorithms.

How?

library(netplot)
library(igraph)

library(igraphdata)
data("UKfaculty")

# Vertex colors f(group)
vcols <- V(UKfaculty)$Group 
vcols <- palette.colors(
  n = length(unique(vcols))
)[vcols]

set.seed(323)
# Netplot call
nplot(
  UKfaculty,
  edge.line.breaks = 20,
  vertex.color     = vcols
  )

How? (cont)

Structure

Graphical objects (Grobs)

List of 11
 $ .xlim        : num [1:2] -1 1
 $ .ylim        : num [1:2] -0.5 0.5
 $ .layout      : num [1:81, 1:2] 0.6661 0.0201 0.7327 0.5399 -0.4903 ...
 $ .edgelist    : num [1:817, 1:2] 57 76 12 43 28 58 7 40 5 48 ...
 $ .N           : int 81
 $ .M           : int 817
 $ name         : chr "graph.3"
 $ gp           : NULL
 $ vp           : NULL
 $ children     :List of 2
  ..$ background:List of 10
  .. ..- attr(*, "class")= chr [1:3] "rect" "grob" "gDesc"
  ..$ graph     :List of 5
  .. ..- attr(*, "class")= chr [1:3] "gTree" "grob" "gDesc"
  ..- attr(*, "class")= chr "gList"
 $ childrenOrder: chr [1:2] "background" "graph"
 - attr(*, "class")= chr [1:4] "netplot" "gTree" "grob" "gDesc"

Example 2: Playing with patterns

netplot supports advanced patterns. The figures feature radial gradients (vertices), lineal gradients, and repeated patterns (background).

Other things to consider

barry in a nutshell

• What: A C++ header-only template library for motif counting (and more.)

• Why: Implement Discrete Exponential Family Models [DEFMs] for phylogenetics and social networks analysis.

• Where: You can get it on GitHub (USCBiostats/barry)

Main features

About 11 K lines of C++ code built for statistical modeling:

• Motif count using change statistics (we will return to that.)

• Full and constrained enumeration of 0/1 arrays.

• Computes probability function for Discrete Exponential-Family Models [DEFMs].

• Memory and computationally efficient for pooled models.

Features: Change statistics

Let’s look into the change statistics edgecount, triangles, and gender-homophily when we remove tie 33-69.

Features: Change statistics (cont.)

Features: Memory and Comp. Efficiency

Modeling

flowchart LR
  start[Create the\nmodel] --> count[Add\ncounters]
  count --> count_done{Done?}
  count_done --> |Yes| const[Add\nconstraints]
  count_done --> |No| count
  const --> const_done{Done?}
  const_done --> |Yes| init((End))
  const_done --> |No| const

flowchart LR
  start[Hash the\narray] --> exists{Present?}
  exists --> |Yes| ptr[[Link\nPointer]]
  exists --> |No| addarray[[Compute\nsupport]]
  ptr --> End((End))
  addarray --> End

Current implemented models

In principle, any dataset we can represent as 0/1 arrays can be modeled with barry. We have applications in social networks, phylogenetics, and health outcomes.

Current implemented models: DEFMs

• DEFMs for multiple correlated outcomes (Markov Random Fields; on development with Drs. MJ Pugh and Tom Valente.)

Current implemented models: Social networks

• Motif counting applied to counting “imaginary motifs” in Cognitive Social Structures [CSS] (with Dr. Kyosuke Tanaka, submitted to Social Networks).

Current implemented models: Phylogenetics

• Modeling the evolution of gene functions in terms of transition between functional states (research grant submitted to National Human Genome Research Institute NHGRI).

Other projects

fmcmc | ergmito | aphylo | netdiffuseR | ABCoptim
slurmR | barry | rgexf | geese

Other projects (cont.)

Thanks!

A1. Change statistics formals

• The change statistic is defined as a real-valued vector where the \(k\)-th entry equals the observed change when the \(ij\)-th tie is removed from the network. Formally:

  \[ \delta(y_{ij}: 0\to 1) = s(\mathbf{y})_{ij}^+ - s(\mathbf{y})_{ij}^- \]

  Where \(s(\cdot)\) is a function returning graph \(\mathbf{y}\)’s observed statistics, and \(s(\mathbf{y})_{ij}^+\) represents its value when \(y_{ij} = 1\).

A1. Change statistics formals (cont.)

Furthermore, conditioning on the rest of the network (or array,) a tie transition probability equates a logit:

\[\begin{equation} \mbox{logit}\left({\mathbb{P}\left(y_{ij} = 1|y_{-ij}\right) }\right) = {\theta}^\mathbf{t}\Delta\delta\left(y_{ij}:0\to 1\right), \end{equation}\]

\[\begin{equation} {\mathbb{P}\left(y_{ij} = 1|y_{-ij}\right) } = \frac{1}{1 + \mbox{exp}\left\{-{\theta}^\mathbf{t}\Delta\delta\left(y_{ij}:0\to 1\right)\right\}} \end{equation}\]